It is known that there is an infinite family of general pretzel knots, each of which has Rasmussen s-invariant equal to the negative value of its signature invariant. For an instance, homologically -thin knots have this property. In contrast, we find an infinite family of 4-strand pretzel knots whose Rasmussen invariants are not equal to the negative values of signature invariants.

Keywords

Rasmussen invariant;knot signature;pretzel knot;

Language

English

Cited by

References

1.

T. Abe and K. Kishimoto, The dealternating number and the alternation number of a closed 3-braid, J. Knot Theory Ramifications 19 (2010), no. 9, 1157-1181.